3.6 Going further

Readers who are interested in obtaining information about the current status of existence theorems in
general relativity are referred to Rendall’s Living Reviews article [137].

Although we have restricted ourselves to the case of a vanishing cosmological constant this does
not mean that other cases have not been analyzed. Friedrich [62] has shown the existence of
asymptotically simple de Sitter type solutions of the Einstein-Maxwell–Yang–Mills equations and
stability of de Sitter space. More recently [64], with the general version of his conformal field
equations, he was able to demonstrate the existence of asymptotically simple anti-de Sitter type
solutions.

It should also be mentioned that some work has gone into generalizing the Bondi–Sachs calculations to
poly-homogeneous space-times [34, 160, 161].

The structure of space-like infinity has been discussed here only in a rather cursory way. A very recent
account of the relationship between static solutions and the role they play can be found in [70]. Readers
who are interested in a more detailed treatment of the subject in general are referred to a recent review by
Friedrich [68].